Speaking to the Schweiz am Sonntag, Maudet, responsible for security in Geneva, said the police officer who is first on the scene must be able to neutralize a terrorist immediately, without having to wait for a specially trained unit to arrive.
“We saw that in Nice. Every police officer must be able to stop a crazed killer immediately. He has to open fire before something worse happens,” he said.
The cantons of Geneva, Vaud and Valais have already changed their operational policy to reflect this, “but that's not enough,” he said, calling for a change to the "basic education" of police officers, Swiss-wide.
“We cannot afford to be unprepared”.
Fellow politicians agree that Switzerland must do more.
Speaking to the Tribune de Genève, Hughes Hiltpold of the liberal-radicals (FDP) said: “I have the impression that we are not ready. The police are the first on the scene. They must be able to react quickly.”
Roger Golay, of the Swiss People's Party (SVP) agreed.
“At the moment each canton does its own thing. We must have a national policy, a plan that can be put in place immediately.... If there was a wave of attacks today in Switzerland, the police would be completely overwhelmed”.
At least two Swiss died in the attack on Bastille Day when Tunisian truck driver Mohamed Lahouaiej-Bouhlel drove a lorry through crowds gathered on Nice's Promenade des Anglais to watch fireworks, killing 84.
On Friday a 54-year-old woman from Ticino was confirmed killed by the Swiss authorities.
And over the weekend the canton of Vaud reported the death of a six-year-old girl from Yverdon-les-Bains.
Speaking to news agencies, a spokesman for the Vaud police said the young victim's father and two other children – aged eight months and four – were hospitalized after the attack, but that the mother has not yet been identified.
In a statement, the city of Yverdon said it was “with great sadness” that it learnt the news of the death of the young girl, who was of Brazilian origin.
“The town and the communal authorities offer their support and sincere condolences to the family and those close to the victim.”
The authorities said children at the school attended by the girl would be given support as the new school year begins in August.
The canton of Vaud has established a hotline (0848 133 133) for those concerned by the attack and needing psychological support.
In a statement on Friday the federal government said it should not be ruled out that there could be other Swiss victims.
The federal police sent two liaison officers to nice to help the French authorities.
A helpline established by the Swiss defence department is open 24 hours a day on 0800 247 365 or 058 465 3333.
At the federal parliament in Bern and the Swiss embassy in Paris flags were put at half-mast after French President Francois Hollande declared three days of mourning on Saturday.